Very smooth until I got to the bottom center, because "Bashfully" says SHYLY to me much more than COYLY. Also, I'm pretty sure Brian Eno never did anything with ELO, but I'm also pretty sure he never did anything with Einstein's Little Homunculus (the only ELH band I could think of).
"I Just Had Sex" hip-hop singer, along with the Lonely Island
15A
GST comp.
16A
Order at a New Orleans coffeeshop
20A
Nanny's child
21A
Home of Mike the Tiger (Abbr.)
22A
Coca-Cola product whose name was formulated by an IBM 1401 computer tasked generating a list of over 185,000 four-letter words with one vowel (which was later shortened)
24A
Track 13 of Taylor Swift's upcoming "Midnights" album, as revealed on TikTok
27A
Role that Keanu Reeves received in part because Will Smith turned it down in order to shoot "Wild Wild West"
28A
Chaplin lady
29A
"America's Favorite Pasta Sauce Brand"
31A
J.C. ___
33A
Tavern beverages
34A
Steps for "I do"?
35A
Disturbs
36A
Bashfully
Verticales
1D
Targeted
2D
Not in harm's way
3D
Go on and on
4D
___ Lingus
5D
Some residents, shortly
6D
Seasonal character that's been played by Tim Allen and Ed Asner, among others